What’s Cracking?
How image schema combinations can model conceptualisations of
events
Maria M. HEDBLOM1and Oliver KUTZ and Rafael PE ˜NALOZA and Giancarlo GUIZZARDI
Conceptual and Cognitive Modelling Research Group (CORE) KRDB Research Centre for Knowledge and Data
Faculty of Computer Science Free University of Bozen-Bolzano, Italy
Abstract. Image schema profiles are described as clusters of spatiotemporal re-lationships learned from embodied experiences and function as the gathered con-ceptual information for event concepts. Looking at such profiles allows not only to model aspects of human conceptualisation but also offers a method to approach event conceptualisation for more formal purposes. This article investigates this re-search program by looking closer at how humans conceptualise events and speci-fies three combination methods of image schema profiles that each offer different aspects for concept construction. As a proof of concept, we present an in-depth analysis of the classic commonsense reasoning problem of ‘Cracking an Egg’ as a demonstration of how these profiles can be used in formal knowledge represen-tation. This is formalised using the Image Schema Logic, ISLM, a combined logic
targeted at the spatiotemporal relationships present in image schemas.
Keywords. image schemas, events, knowledge representation, event segmentation
1. Introduction
Capturing the nature of events and the dynamic transformations they bring about in the world, is a difficult problem to formally model. However, where formal knowledge rep-resentation struggles, human cognition is a master. Based on experiences, humans have an understanding of ‘what’s cracking’ (i.e.,‘what’s happening’, ‘what’s going on’), even in ongoing and future events with uncertain development and outcome. When there is a mismatch in our conceptualisation of the event we are faced with, we can easily modify this understanding to fit the new situation. When presented with a familiar scenario, e.g., going to the supermarketor borrowing a book at the library, we have a mental general-isation based on all previous experiences (explicit and implicit) with that particular sce-nario, and have a mental space of that concept that we use to verbalise our thoughts when conversing with other people. In the more generic, often-experienced situations human conceptualisation can be argued to be greatly overlapping. For instance, despite cultural
differences, it is likely that all humans share the same, or an indistinguishable, concep-tualisation of the concepts of being hungry and going to sleep. However, for events such as going to war or preparing Turducken,2events most of us never experience first hand,
the conceptualisation may differ greatly.
This flexibility in representing and updating information is not as straightforward for formal knowledge representation. Classic commonsense reasoning problems such as Cracking an Egg [19] often require long and complex axiomatisations that offer little in terms of dynamic alterations (e.g. [24, 19]). In contrast, most human adults have a fair amount of experience with eggs and ‘cracking them’ and, therefore, have exten-sive knowledge of both how an egg breaks, as well as what happens when it does. In this paper, we look at human cognition as an inspiration to approach this problem for knowledge representation. We argue that the conceptualisation of such experiences can be broken down into a common structure using conceptual building blocks, the image schemas[17, 14], based on findings from embodied cognition [28]. To better model the complexity of events we look to image schema profiles [25] as a means to represent the different combinations image schemas can have and introduce three different characters by which these profiles seem to exist. These Image Schema Combinations are then struc-tured and formalised using the Image Schema Logic, ISLM, a multi-dimensional logic
devoted to the spatiotemporal relationships present in image schemas. Finally, we return to the classic commonsense reasoning problem ‘Cracking an Egg’ as a proof of concept.
2. Foundation and Motivation
Deep learning techniques have greatly advanced perceptual and categorical aspects of Artificial Intelligence [27]. However, when it comes to conceptual processes such as understanding and generating concepts and event structures, the advancement does not display the same success. It appears as though the meaning of certain notions cannot be attained through pure korvstoppning.3Instead, conceptual meaning appears to be
as-sociated with uses and purposes of objects and events rather than their perceptible at-tributes and patterns [22]. For instance, while a cup might be visually identified by the combination of a hollow cylinder with a handle, it is the affordance to contain liquid that makes it a cup. Likewise, an event like going to the library can be cored down to ‘per-son walking towards library-building’ as well as core participants therein (i.e., Per‘per-son, Library, Road). But at the same time, we associate a library and going there with a full range of additional conceptual information such as ‘lending/renting,’ ‘book collection,’ ‘knowledge,’ ‘public place,’ etc. Information that in itself is not perceptual but based on particular experience through the affordances the concept realises.
One area of cognitive science aiming to explain the relationship between perception and conceptualisation is embodied cognition [28].4The theory suggests that conceptual meaning is a direct reflection of the generalised information from repeated sensorimotor
2A dish prepared through the iterative stuffing of a chicken into a duck, and the duck into a turkey. 3Korvstoppning is a Swedish idiom roughly translating to ‘sausage cramming.’ It captures the notion of
overfeeding a person with information without allowing for any real understanding to take place.
4Note that embodied cognition is a family of theories with similar theses. As this paper does not care for the
experiences. While this theory has a fair amount of support from different directions (e.g., [4, 21]), it does not in itself provide a concrete description for how or where the conceptual information is stored. Instead, what it does provide is a framework in which conceptual processes can be viewed as a reflection of perceptual ones. When looking at the repeated perception of particular events, humans learn early how to distinguish different events from one another, as well as to ‘break apart’ conceptual parts from the events that are more or less irrelevant for the purposes of that particular event type. In the next section, we investigate some early stages of how humans identify events in an endless flow of perceptive information.
2.1. Event Perception and Segmentation
Objects can be distinguished by how they can be separated from other objects in their sur-roundings. Gestalt laws often dictate how objects relate to one another and which percep-tive stimuli belong to which particular objects. Simultaneously the theory of recognition-by-parts suggests that objects are ‘mentally broken down’ into geometric shapes as a means of identification and categorisation [2]. In comparison, a common view of events is that they are fourth-dimensional entities [18]. While this view is too rigid to elegantly handle formal representation of the transformations in ongoing or future events, it does provide a starting point to investigate human event conceptualisation and its formal cor-respondence. One important distinction when drawing parallels between object and event perception is that, unlike for objects, there are no ‘borders’ in the passing of time. One event often floats seamlessly into another without pauses, beginnings or ends. They can and are often overlapping and it is unclear which parts are events in themselves or simply parts of other events. Additionally, as discussed in [8], different ‘parts’ of an event seem to have different degrees of significance. For instance, in the event the death of Caesar, Caesar’s participation seems to be conceptually much more important than the daggers’ participation.
Research on event individuation demonstrates that initially the events are distin-guished by their end-states [31], i.e., Caesar being dead in the example above. However, as cognitive maturity develops a more fine-grained understanding of the individual parts and processes of particular events are learned. [1] demonstrates that infants presented with an ‘event break’ appear to have difficulty to perceive the full scenario as one event, regardless of the end state. [6] performed experiments investigating event and action in-dividualisation abilities in toddlers only to discover that children are early capable of separating actions within events from the event as a whole. [29] performed experiments providing support for the notion that not only objects (and actions) are segmented but also the paths that objects move along go through the same kind of segmentation process. Another classic study made with three-months-olds showed that infants are at that age already able to make predictions and anticipate events based on their particular structure [9].
spatial or material, can then, in different combinations represent increasingly complex and large-scale events.
Research in cognitive linguistics also demonstrate these tendencies as there exists a range of different theories to explain how information is broken into smaller conceptual structures (e.g., Semantic Primes [32]). One promising theory that gathers research on embodied cognition, cognitive linguistics and developmental psychology is the theory of image schemas [14, 17]. As these conceptual building blocks are central to the present hypothesis they will be thoroughly presented below.
3. Image Schemas
Image schemas represent the abstract generalisations learned from the sensorimotor pro-cesses [17, 14]. They are conceptual gestalts, meaning that each part is essential for the whole meaning of the image schema,5and most often they are described as cap-turing sensorimotor relationships and their transformations. LINK6, CONTAINMENTand CENTER PERIPHERY are examples of static image schemas but transformations such as LINKED PATH, Going INand REVOLVING MOVEMENTare also image schematic. The idea with image schemas is that they provide a bridge between perceptive experi-ences and conceptual expressions found in natural language. For instance, time is often described using spatial PATHs (“time moves on”) and love is often conceptualised as CONTAINER(“falling in love”).
In regards to object and event conceptualisations, image schemas are thought to be structured into image schema profiles defined as groupings of image schemas that capture the spatiotemporal relationships related to particular events [25]. Below, this phenomenon is further introduced.
3.1. Image Schema Profiles
[25] describes how Image Schema Profiles are a collection of image schemas that to-gether describe the conceptualisation of particular events and concepts. For instance, in [7] the authors provide a plethora of image schema profiles for the word stand based on different linguistic contexts. Image schema profiles work in the following manner: if I am to describe the image schema profile of the event going to the supermarket, I might describe it using a collection of: SOURCE PATHGOAL—as I am going to the supermar-ket; CONTAINMENT—as myself and the groceries are inside the building, PART WHOLE
and COLLECTION—as there are plenty of pieces in the supermarket and I collect them, TRANSFER—as I am obtaining objects from the supermarket to my own ‘person;’ etc. Likewise, although I never cooked Turducken, I can conceptualise the process of prepar-ing the dish through an image schema profile largely consistprepar-ing of: goprepar-ing IN—as the chicken goes into the duck, and the duck goes into the turkey; CONTAINMENT—as the animals remain inside ‘each other;’ ITERATION—as this process is repeated three times; and SCALE—as the chicken, the duck, and the turkey are treated in their respective sizes. Naturally, an expert chef frequently preparing the dish might understand that there is more at work.
5For instance, consider a container without an inside.
Image schema profiles are one way in which the conceptualisation of particular sce-narios and events can take place. However, note that image schema profiles are not hier-archal or temporally structured like Schankian scripts. Rather, image schema profiles are collections without explicit internal structure or order. While this is the cognitive reality of the profiles, with the intention to use the profiles for formal knowledge representation, it is beneficial to internally organise the image schemas in a more structured manner. In the next section, we introduce three ways image schemas can be combined.
3.2. Image Schema Combinations
Image schemas can be combined with one another in many different ways. To illustrate this we back-trace from a few concepts and real-world events into their image-schematic construction. One of the most common ways to conceptualise the passing of time is to make an analogy to the spatial dimension in a 2D world, basically a ‘path.’ For in-stance, marriage is often perceived as two people walking together through life [22]. Basically embodying the combination of the image schemas SOURCE PATHGOALand LINK. In a (traditional) marriage what happens to one of the parties, arguably also af-fects the other. This means that the gestalt properties of the image schemas are merged into LINKED PATH, an image schema in its own right. In another scenario, with the con-cept of transportation, the concon-ceptualisation is treated more as a collection of image schemas, in this case, SOURCE PATH GOALand SUPPORT (or CONTAINMENT) [15]. This is particularly interesting because, like how a cup is ‘defined’ by the affordance of CONTAINMENT, it illustrates how image schemas also become part of the definition of more abstract concepts.
Another metaphorical example is the idiom to hit the wall. In many contexts, this does not mean to physically crash into a wall but instead implies some form of mental or physical breakdown. The idiom captures the image schema of BLOCKAGE. It is clear that BLOCKAGEis not an atomic image schema but rather a sequential combination of several ones (see [12] for an in-depth analysis). Breaking it down, there are at least two OBJECTs, a SOURCE PATH GOAL, and at least one time-point when the two objects are in CONTACT. Translating it to a natural language expression: The OBJECTs represent the person and the abstract time point and/or scenario with which the person ‘crashed,’ so to speak, and this moment captures an abstract version of the image schema CONTACT.
As demonstrated, this kind of image-schematic breakdown can be done not only on concrete scenarios but also on many abstract natural language expressions. The men-tioned examples lead to primarily three different ways in which image schemas can be combined (see Fig. 1):
Merge: Occurs when two image schemas are combined in such a way that the Gestalt laws are altered.7
Collection: A collection of image schemas do not, per se, alter the Gestalt properties of a particular spatiotemporal relationship, but instead functions as a joint repre-sentation for a particular concept. This is the most classic form of image schema profiles.
7In [13, 12] the authors suggest that image schemas can be structured as interlinked families of theories.
(a) Merging (b) Collection (c) Sequence
Figure 1. The three different ways image schemas can be combined.
Sequence: This represents the image-schematic conceptualisations that behave much like collection, only with the addition of a sequential ‘cause-and-effect’ dimension. In many cases, this takes a linear form but there are situations with branching routes or circular patterns.
3.3. Formal Representation UsingISLM: The Image Schema Logic
While image schemas are cognitive patterns without any concrete formal correspon-dence, there exist attempts to capture them formally (e.g., [15, 5]). In [12], an approach towards an expressive logical language devoted to image schemas, ISLM, was intro-duced.8Simplified, ISLMis an expressive language building on the Region Connection Calculus (RCC) [26], Ligozat’s Cardinal Directions (CD) [20], Qualitative Trajectory Calculus (QTC) [30], with 3D Euclidean space assumed for the spatial domain, and Lin-ear Temporal Logic over the reals (RTL). The work on formalising the individual image schemas and their dynamic transformations in this logic has been initiated, for instance, in [11]. Due to page limitation, we refrain from further elaboration of the logic and for a more detailed account, we refer instead to previous publications.
Formalising the image schemas using the ISLMlanguage makes it possible to repre-sent the individual image schemas and by taking their spatial, and temporal, primitives (such as PATH, OBJECT, OUTSIDEand INSIDE[23]) into account similar image schemas can be grouped together into ‘families’ represented as graphs of theories with increasing complexity [13]. The latter provides a means to investigate the merged combinations of image schemas by looking at the intersection of two different image schema families (ie. ‘Going IN’ would lie at the intersection of SOURCE PATHGOALand CONTAINMENT). The collection of formalised image schemas and their spatial components can be seen as a repository of cognitively-based ontology design patterns [3] that can be used when building conceptualisations of concepts and events. In the next section, we illustrate this phenomenon by generating image schema profiles for Egg-Cracking.
4. Studies in Egg-Cracking with Image Schema Combinations
In the introduction one of the prototypical knowledge representation problems ‘cracking an egg’ was introduced as an event that is conceptually rather simple but highly complex to formally model. Following the reasoning in this paper, it is possible to utilize image schema profiles, or their more structured versions image schema combinations, as a way to represent conceptual information. Below we look at two different scenarios.
8In [10], this language was further developed under the name ISLFOLby the addition of a First-Order concept
(a) Scene 1: The egg is supported by a hand. (b) Scene 2: The egg is no longer supported, i.e. dropped. (c) Scene 3: The egg falls to the ground.
(d) Scene 4: The egg hits the ground.
(e) Scene 5: The egg breaks.
Figure 2. Event Segmentation of Dropping an Egg.
4.1. Dropping an Egg
Infants do not have enough experience with the object ‘egg’ to immediately understand that if you drop it, it falls and as it hits the ground it (usually) breaks. This we learn as we get more and more experience in the kitchen, or at chicken farms. While all temporally dependent scenarios happen in more or less a sequence without defined borders, based on the findings presented in Section 2.1, the event can be divided into conceptually distinct steps (see Fig. 2). One important hypothesis is that for each step a conceptually different scene of undefined temporal length takes place. This translates into there being an image-schematic alteration or transformation at work. The scenario can be described with a sequentialimage schema combination based on the following scenes:
1. The egg is SUPPORTed by a hand.9
2. The egg is no longer SUPPORTed. Note that in most natural cases there is still CONTACTbetween the hand and the egg at this stage. In a human conceptuali-sation, it is likely that this event takes place more or less simultaneously as the consecutive scene in which . . .
3. . . . the egg falls from the SOURCE: hand, to the GOAL, where Falling is a merge between SOURCE PATH GOAL and VERTICALITY as the gestalt properties of each image schema rely on one another.
4. The egg is BLOCKEDby the ground, stopping its SOURCE PATHGOAL. 5. The final scene is an image-schematic transformation of SPLITTING. In which
the WHOLE(egg) → PARTs(egg),10 and the egg remains SUPPORTed by the ground.11
Following the idea behind the ISLMlanguage, each image schema can be formalised
as a design pattern that can be referenced in different situations. In [10] a large selec-tion of these image schema patterns can be found. Due to page limitaselec-tion we limit our formalisation to capture the overlaying patterns and only report on a few of them (see 9Here it is possible to substitute SUPPORTfor CONTAINMENTif the egg is ‘grabbed’. This would alter the
properties of the agent’s involvement in the ‘drop’.
10In ISLMDC means DisConnected (based on RCC8) and U, is taken from LTL and denotes ‘Until’. Thus,
the image schema SPLITTINGcan be formalised in the following manner:
∀X, x1, x2: Ob ject SPLITTING(x) → WHOLE(X ) ∧ Part(x1, X ) ∧ Part(x2, X ) U¬WHOLE(X ) ∧ DC(x1, x2)
11Note that this is due to the BLOCKAGErelation from the previous scene, only now, the force is removed
(a) Scene 1: The egg and bowl are separated.
(b) Scene 2: The egg moves towards the bowl’s border.
(c) Scene 3: The egg hits the bowl’s border.
(d) Scene 4: The egg cracks.
(e) Scene 5: The egg moves to the top of the bowl.
(f) Scene 6: The egg separates into parts.
(g) Scene 7: The egg0 leaves the shell and falls.
(h) Scene 8: The egg0falls.
(i) Scene 9: The egg0 enters the bowl.
(j) Scene 10: The egg0 is inside the bowl.
Figure 3. Event Segmentation of Cracking an Egg into a Bowl.
Footnote12). In ISLMthe entire event could be formalised as follows:
∀Egg:Ob ject, ∀Hand, Ground:Region Dropping an egg → SUPPORT(Hand, Egg) U (¬SUPPORT(Hand, Egg) ∧ CONTACT(Hand, Egg)) U (On PATHToward(Egg, Ground)) ∧ ¬CONTACT(Hand, Egg)) U (BLOCKED(Egg, Ground) ∧ ¬On PATHToward(Egg, Ground)) U (SPLITTING(Egg) ∧ SUPPORT(Ground, Egg))
4.2. Cracking an Egg into a Bowl
In most scenarios where there is an intention to crack the egg, this is done by gather-ing the contents in a bowl. We argue here that such an event can be divided into ten conceptually distinct spatiotemporal scenes (depicted in Fig. 3):
1. Scene one presupposes two OBJECTs: an egg and a bowl. The bowl is a CON
-TAINER and represents the egg’s GOAL location. Additionally, the egg needs to be described as a WHOLE with two PARTs: the shell (CONTAINER) and an egg013(CONTAINed). This is a conceptual merge between CONTAINMENTand PART WHOLE.14
12∀O
1, O2:Ob ject (CONTACT(O1, O2) ↔ ¬DC(O1, O2))
∀O1, O2:Ob ject (SUPPORT(O1, O2) ↔ EC(O1, O2) ∧ Above(O1, O2) ∧ Forces(O1, O2))
∀O1, O2:Ob ject On PATHToward(O1, O2) ↔ (O1 O2∧ outside of(O1, O2))
13While in natural language both the whole egg and its content is referred to as an egg, we need to formally
distinguished them. Thus, we refer to the whole egg as egg and the content as egg0.
14For eggs, it is rather straightforward that the part that we use is on the inside of the shell, however, consider
2. Scene two has all the same properties as scene one, with the addition of SOURCE PATH GOALas the egg is moving from its original position towards the edge of the bowl.
3. As the egg hits the border of the bowl, the movement is BLOCKED. This means that instead of the previous SOURCE PATH GOAL image schema, the image-schematic relationship is that of BLOCKAGE. As the egg hits the edge of the bowl, it is intended to crack. However, conceptually this is a different event component that may or may not take place, dependent on how hard the impact between the bowl and the egg was. Then . . .
4. . . . the egg cracks: breaking from a WHOLE into PARTs: the shell and the egg0. This is an image-schematic transformation of PART WHOLE. While this event may be perceived to happen simultaneously as the third scene, it is conceptually different as the properties of the egg suddenly are altered. Likewise, if not enough force has been applied there is no guarantee that the egg cracks or if too much force has been applied the egg0pours out all over the bowl’s edge (considerations on force is addressed in Section 4.3).
5. Still CONTAINed in the cracked shell, the egg0moves towards the bowl’s opening. A scene that functions as a collection (as neither is dependent on the other) and captures both CONTAINMENTand SOURCE PATH GOAL.
6. Removing the CONTAINMENTschema of the egg, by SPLITTINGthe shell from the egg0through the existence of their PART WHOLErelationship.
7. As a merge, the egg0goes OUTfrom the shell and begin to fall towards the bowl’s INSIDE.
8. The egg0continues to fall towards the bowl’s inside.
9. Still moving, the egg0falls into the bowl: the merge between going INand the pre-existing merge of falling based on SOURCE PATH GOALand VERTICAL
-ITY.
10. Finally, the scenario ends with static CONTAINMENTin which the egg0rests in-side the bowl.
∀Egg, Bowl, Egg0:Ob ject, ∀Hand, Bowl, Bowlop, Shell:Region cracking an egg → (Contained Inside(Hand, Egg) ∧ WHOLE(Egg) ∧ PART(Shell, Egg)∧ PART(Egg0, Egg) ∧ Contained Inside(Egg0, Shell)) U (Contained Inside(Hand, Egg)) ∧ On PATH Toward(Egg, Bowl) U (Contained Inside(Hand, Egg) ∧ BLOCKAGE(Egg, Bowl)) U (Contained Inside(Hand, Egg) ∧ ¬WHOLE(Egg)) U (Contained Inside(Hand, Egg) ∧ On PATHToward(Egg, Bowlop)) U (SPLITTING(Egg))
U (going OUT(Shell, Egg0) ∧ On PATHToward(Egg0, Bowl)) U (On PATHToward(Egg0, Bowl)) U (On PATH Toward(Egg0, Bowl)) ∧ going IN(Egg0, Bowl)) U (Contained Inside(Egg0, Bowl)
4.3. The Problem of Force in Egg-Cracking
One of the limitations of the egg-cracking scenarios presented above is that they both represent the ideal “successful” scenario. In a natural scenario, for an egg falling to the ground, little can go ‘wrong’ with the exception that the egg might not actually break. This could be the result of an unusually hard shell, a ‘soft landing’ on a carpet or that it has been dropped at a distance too short for the accumulated force from gravity to break the egg. All of this comes down to one physical component force. Image schemas have a lot of force relations built into them. For instance, SUPPORTrelies on the notion that enough force keeps the object in place, and BLOCKAGEcaptures the counterforce equiv-alent (or stronger) present in the movement. In [23], the authors describe the concept of force as a conceptual add-on to image schemas. When modelling any scenario, propo-sitional add-ons such as the hardness of the shell or the ground, the height of the drop or the force by which the egg hits the bowl can be attached to the individual scenario to provide a more detailed account of the scenario. This way, the image schemas construct the skeletal information and details, perceptive descriptions and characteristics can be added to flesh out the event conceptualisation for a richer description.
5. Discussion and Conclusion
combinations capture some of the most apparent combinations of image schemas, they are by no means intended to be exhaustive. Other combinations, or even combinations of these combinations, are possible to exist that was not considered for the purposes of this paper. These profiles were then formalised using ISLM, a logical language especially developed to deal with the spatiotemporal dimensions of image schemas.
As the focus of this paper was not to introduce the logical language nor to present the audience with a repository of formalised image schemas, both of these aspects were mentioned only in passing through references to previous literature and footnotes. In a future paper, we intend to further explore on how image schema, image schema profiles and their combinations formalised using ISLMcan serve as cognitively-inspired Ontology Design Patterns[3] for the representation of events. However, in order to do that, a more complete repository is required. At the moment, formalisations of the image schemas are largely limited to the families SOURCE PATHGOAL, CONTAINMENTand the static ‘two-object’ relationships (CONTACT, SUPPORTand LINK) [10]. Naturally, for a more complete representation of image schema profiles and the conceptualisation of events, more image-schematic patterns are required.
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